Sample Size Calculation For Cohort Study

Sample Size Formula for Comparing Proportions:

\[ n = \frac{Z^2 \times (p_1(1-p_1) + p_2(1-p_2))}{d^2} \times (1 + \frac{1}{k}) \]

Z-Score (Z):

unitless

Proportion 1 (p1):

proportion

Proportion 2 (p2):

proportion

Effect Size (d):

effect size

Allocation Ratio (k):

ratio

Required Sample Size (n):

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1. What Is Sample Size Calculation For Cohort Study?

Sample size calculation for cohort studies determines the number of participants needed to detect a specified effect size with adequate statistical power. This calculation ensures the study has sufficient sensitivity to identify meaningful differences between groups while controlling for Type I and Type II errors.

2. How Does The Calculator Work?

The calculator uses the sample size formula for comparing proportions:

\[ n = \frac{Z^2 \times (p_1(1-p_1) + p_2(1-p_2))}{d^2} \times (1 + \frac{1}{k}) \]

Where:

\( n \) — Required sample size
\( Z \) — Z-score corresponding to desired confidence level
\( p_1 \) — Proportion in group 1
\( p_2 \) — Proportion in group 2
\( d \) — Effect size (minimum detectable difference)
\( k \) — Allocation ratio between groups

Explanation: This formula calculates the sample size needed to compare two proportions in cohort studies, accounting for the desired statistical power, confidence level, and group allocation.

3. Importance Of Sample Size Calculation

Details: Proper sample size calculation is essential for study validity. An underpowered study may fail to detect true effects, while an overpowered study wastes resources. This calculation ensures optimal resource allocation and scientific rigor.

4. Using The Calculator

Tips: Enter Z-score (typically 1.96 for 95% CI), expected proportions for both groups, the minimum effect size you want to detect, and the allocation ratio between groups. All values must be valid (proportions between 0-1, positive effect size and allocation ratio).

5. Frequently Asked Questions (FAQ)

Q1: What Z-score should I use?
A: For 95% confidence level, use Z=1.96; for 90% confidence, use Z=1.645; for 99% confidence, use Z=2.576.

Q2: How do I determine expected proportions?
A: Use literature values, pilot study results, or clinical expertise to estimate the proportions you expect to see in each group.

Q3: What is a reasonable effect size?
A: The effect size should represent the minimum clinically important difference. Smaller effect sizes require larger sample sizes.

Q4: How does allocation ratio affect sample size?
A: Equal allocation (k=1) is most efficient. Unequal allocation increases total sample size but may be necessary for practical reasons.

Q5: Should I adjust for multiple comparisons?
A: If testing multiple hypotheses, consider using a more conservative alpha level or adjusting the sample size accordingly.